$\begingroup$Why do you include a quasi-linear form of utility function in the title? Is quasi-linearity supposed to have any significance in your question? By "boundary condition" did you mean "corner solution"?$\endgroup$
– Herr K.Jun 4 '19 at 20:29

$\begingroup$When you ask about the optimal bundle as a function, you probably mean as a function of parameters, but which parameters are you considering?$\endgroup$
– RegioJun 5 '19 at 20:10